The only way to get a free drink in this bar, is to prove to the barman that you are a friend of his boss. Here's how its done. You go to the barman, he tells you a number and you tell him the "countersign" number. If your answer is correct you get your drink. There's this mathematician who thought that there can't be a standard list of numbers and countersign numbers. There must be an algorithm that provides the answer from the number given by the barman. So he joins a party of three men who ARE friends of the boss and walks with them to the bar hopping to understand the algorithm from the three answers. HERE'S WHAT HE HEARD: The barman says "6" to the first man, he says "3" and got his drink. The barman said "12" to the second man, who replied "6" and got his drink. The barman said "14" to the third man and he answered "8" (!) and got his drink. Now its the mathematicians turn. "20", said the barman. What is the counter sign?

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Solution:

Six

You count the number of letters in the word. Twenty has 6 letters so the mathematician should say "six".